WASHINGTON — In an argument that touched on medical science and moral philosophy, the Supreme Court on Tuesday wrestled with whether corporations may refuse to provide insurance coverage for contraception to their workers based on the religious beliefs of the corporations’ owners.

The court seemed ready to accept that at least some for-profit corporations may advance claims based on religious freedom. But the justices appeared divided along ideological lines over whether the objections before it, based on a requirement in President Obama’s health care law, should succeed.

Justice Anthony M. Kennedy, who probably holds the decisive vote, asked questions helpful to both sides. He appeared skeptical that the two family-controlled companies that objected to the contraception coverage requirement were burdened by the law, as they could cease providing health insurance at all. He also expressed solicitude for “the rights of the employees.”

But Kennedy also had reservations about whether the government could require the companies in the case to provide coverage in light of the many exemptions and accommodations it has offered to other groups.

The lower courts are divided over whether corporations may object to generally applicable laws on religious liberty grounds.

In June, the US Court of Appeals for the 10th Circuit, in Denver, ruled for Hobby Lobby, a corporation owned by a family whose members have said they try to run the business on Christian principles. The company, which operates a chain of arts-and-crafts stores and has more than 13,000 full-time employees of many faiths, objected to a requirement in Obama’s health care law that large employers provide their workers with comprehensive insurance coverage for contraception.

Hobby Lobby told the justices that it had no problem offering coverage for many forms of contraception and sterilization surgery. But drugs and devices that may prevent embryos from implanting in the womb are another matter, the company said; its owners believe those would make the company complicit in a form of abortion.

Failure to offer comprehensive coverage could leave it subject to fines of $1.3 million a day, Hobby Lobby said, while dropping insurance coverage for its employees entirely could lead to fines of $26 million a year. Those choices, the company said, placed a burden on its owners’ religious beliefs in violation of the Religious Freedom Restoration Act of 1993.

In July, the US Court of Appeals for the Third Circuit, in Philadelphia, ruled against the Conestoga Wood Specialties Corp., which makes wood cabinets and is owned by a Mennonite family that had similar objections to the law. The Third Circuit concluded that “for-profit, secular corporations cannot engage in religious exercise.”

The Third Circuit rejected an analogy to the Supreme Court’s 2010 decision in Citizens United, which said corporations have a First Amendment right to free speech. Though the First Amendment also protects the free exercise of religion, Judge Robert E. Cowen wrote for the majority of a divided three-judge panel, “it does not automatically follow that all clauses of the First Amendment must be interpreted identically.”

But a five-judge majority of an eight-judge panel of the 10th Circuit, in the Hobby Lobby case, said that “the First Amendment logic of Citizens United” extended to religious freedom.

“We see no reason the Supreme Court would recognize constitutional protection for a corporation’s political expression but not its religious expression,” Judge Timothy M. Tymkovich wrote for the majority.

A dissenting member of the court, Chief Judge Mary Beck Briscoe, wrote that the majority’s approach was “nothing short of a radical revision of First Amendment law.”

The Obama administration has exempted many religious groups from the coverage requirement, which is part of the Affordable Care Act. But it said that for-profit corporations could not rely on religious objections to opt out of compliance with the law.

Tuesday’s arguments took place almost exactly two years after the arguments in a challenge to another part of the Affordable Care Act. The Supreme Court upheld that provision, which requires most Americans to obtain health insurance or pay a penalty.

A decision in the new cases — Sebelius v. Hobby Lobby Stores, No. 13-354, and Conestoga Wood Specialties v. Sebelius, No. 13-356 — is expected by the end of June.

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